EECS130 Integrated Circuit DevicesAnnouncementsSlide Number 3Slide Number 4Ideal MOS CapacitorIdeal MOS Capacitor At Equilibrium:Ideal MOS Capacitor Under BiasP-type Si, VG < 0 (accumulation)P-type Si, VG < 0 (accumulation)p-type Si, VG > 0 (depletion)p-type Si, VG >> 0 (inversion)Inversion conditionSlide Number 13Ideal MOS Capacitor – n-type SiSlide Number 15Electrostatic potential, (x)Electrostatic potentialQuestionCharge Density - AccumulationCharge Density - DepletionCharge Density - DepletionQuestion?Charge Density - InversionGate Voltage RelationshipGate Voltage RelationshipSlide Number 26EECS130 Integrated Circuit DevicesProfessor Ali Javey10/09/2007MOS Cap, Lecture 1Reading: finish chapter16Announcements• Exam Results…MOS Capacitors (MOSC)MOS: Metal-Oxide-SemiconductorSiO2metalgateSi bodyVggateSi-body (P)N+MOS capacitorMOS transistorVgSiO2N+Chapter 16MOS transistor is the most important device in modern microelectronics.Ideal MOS Capacitor– Oxide has zero charge, and no current can pass through it.– No charge centers are present in the oxide or at the oxide- semiconductor interface.– Semiconductor is uniformly doped– ΦM = ΦS = χ + (EC – EF )FBIdeal MOS Capacitor At Equilibrium:Ideal MOS Capacitor Under Bias– Let us ground the semiconductor and start applying different voltages, VG , to the gate– VG can be positive, negative or zero with respect to the semiconductor – EF,metal – EF,semiconductor = – qVG– Since oxide has no charge (it’s an insulator with no available carriers or dopants), d Eoxide / dx = ρ/ε = 0; meaning that the E-field inside the oxide is constant.P-type Si, VG < 0 (accumulation)εECEiEVEFsGqVmΦAccumulationof holesconst.0oxideoxide=⇒=∂∂EEx•The oxide energy band has constant slope as shown. •No current flows in the SiO2 layer ÎEFin Si is constant.Negative voltage attracts holes to the Si-oxide interface.This is called accumulation condition.Ei –EF shouldincreases near thesurface of Si.P-type Si, VG < 0 (accumulation)– – – –+ + Sheet of holesρEMOSVG < 0Sheet ofelectronsxAccumulation of holes nearsilicon surface, and electronsnear the metal surface.Similar to a parallel platecapacitor structure.p-type Si, VG > 0 (depletion)EFMECEiEFsEVDepletionEOM Spositive=ρ0=ρnegative=ρ+++- ---- ---Ep-type Si, VG >> 0 (inversion)ECEiEVEFM++++----------------Immobile acceptorsMobile electronsEFMEFSEInversion conditionIf we continue to increase the positive gate voltage, the bands at the semiconductor bends more strongly. At sufficiently high voltage, Ei can be below EF indicating large concentration of electrons in the conduction band.We say the material near the surface is “inverted”. The “inverted” layer is not gotten by chemical doping, but by applying E-field. Where did we get the electrons from?When Ei (surface) – Ei (bulk) = 2 [EF –Ei (bulk)], the condition is start of “inversion”, and the voltage VG applied to gate is called VT (threshold voltage). For VG > VT , the Si surface is inverted.Ideal MOS Capacitor – n-type SiElectrostatic potential, φ(x)Define a new term, φ(x) taken to be the potential inside the semiconductor at a given point x. [The symbol φinstead of V used in MOS work to avoid confusion with externally applied voltage, V])]((bulk)[1)(iixEEqx −=φ(surface)](bulk)[1iiSEEq−=φ](bulk)[1FiFEEq−=φPotential at any point xSurface potentialφF > 0 means p-type φF < 0 means n-type| φF | related to doping concentrationElectrostatic potentialφS = 2φF at the depletion-inversiontransition point (threshold voltage)φS is positive if the bands bend\ …….?QuestionConsider the following φF and φS parameters. Indicate whether the semiconductor is p-type or n-type, specify the biasing condition, and draw the energy band diagram at the biasing condition.(i) φF = 12 kT/q; φS = 12 kT/q(ii) φF = −9 kT/q; φS = −18 kT/qCharge Density - Accumulationp-type silicon accumulation conditionThe accumulation charges in the semiconductor are ……. , and appearclose to the surface and fall-offrapidly as x increases.One can assume that the free carrier concentration at the oxide- semiconductor interface is a δ-function.M O SVG < 0p-SiAccumulation of holesCharge on metal = −QM Charge on semiconductor = −(charge on metal) |QAccumulation | = |QM |xCharge Density - Depletionp-type Si, depletion conditionThe depletion charges in Si are immobile ions - results in depletionlayer similar to that in pnjunction or Schottky diode.VG > 0M O Sp-SiDepletion of holeswQM|q NA A W| = |QM |(−)(+)If surface potential is φs , then the depletion layer width W will beSASi2φεqNW =Does this equation look familiar?Charge Density - DepletionFor a p+n junction, or a MS (n-Si) junction, the depletion layer width is given by:biDSi2VqNWε=Where Vbi is related to the amount of band bending. Vbi in Volts is numericallyequal to the amount of band bending in eV.biSiDSiDmax2VqNWqNε−=ε−EFor MOS, the same equation applies, except that Vbi is replaced by φs.||2or||2Si)(insSiAsSiDmaxφεφε−=qNqNEn-typep-typeQuestion?• What Vg gives you the maximum possible depletion width in a MOSC?Charge Density - InversionVG >>0M O Sp-SiDepletion of holeswQMInversion electrons:δ-function-likep-type Si, strong inversionOnce inversion charges appear, they remain close to the surface since they are …….. Any additional voltage to the gate results in extra QM in gate and get compensated by extra inversion electrons in semiconductor. So, the depletion width does not change during inversion. Electrons appear as δ- function near the surface. Maximum depletion layer width W = WTGate Voltage RelationshipApplied gate voltage will be equal to the voltage drop across the oxide (insulator) plus the voltage across the semiconductor. Consider p-type Si.VG > 0M O Sp-Si ΔφSemi ΔφoxVG = Δφox + ΔφSemi ΔφSemi = φ(x = 0) −φ(bulk)= φS Δφox = xox EoxSince the interface does not have any charges (idealized MOSC), we can say that: εox Eox = εSi ESiEox = (εSi / εox ) ESiWhen is this equation valid?Gate Voltage RelationshipsSiAFssASiSiASiASi220for2φεφφφεεεqNqNqNWqN=<<==EFssSiAoxSioxsSioxSioxsoxoxsG20for2φ≤φ≤φεεε+φ=εε+φ=+φ=qNxxxVEEQuestionDraw E vs x for an ideal MOSC for the case of depletion and
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